Premium
Carleman estimates and unique continuation for second‐order elliptic equations with nonsmooth coefficients
Author(s) -
Koch Herbert,
Tataru Daniel
Publication year - 2001
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/1097-0312(200103)54:3<339::aid-cpa3>3.0.co;2-d
Subject(s) - order (exchange) , mathematics , citation , library science , algebra over a field , computer science , pure mathematics , finance , economics
In this work we obtain strong unique continuation results for variable coefficient second order parabolic equations. The coefficients in the principal part are assumed to satisfy a Lipschitz condition in x and a Holder C 1 3 condition in time. The coefficients in the lower order terms, i .e. the potential and the gradient potential, are allowed to be unbounded and required only to satisfy mixed norm bounds in scale invariant LptLqx spaces. The evolution of the understanding of the strong unique continuation prob- lem for second order parabolic equations mirrors and is closely related to the corresponding strong unique continuation problem for second order elliptic equations. Consequently, we begin with a brief overview of the latter problem. To a second order elliptic operatorg = ∂igij∂j and potentials V , W in Rn we associate the elliptic equation